Alves and Batista extended
several results from the theory of partial group actions to the Hopf algebra setting, they constructed
a Morita context relating the fixed point subalgebra for partial actions of finite dimensional Hopf
algebras, and constructed the partial smash product in [1]}. Later, they constructed a Morita context between the partial smash
product and the smash product related to the enveloping action, defined partial representations of Hopf algebras and
showed some results relating partial actions and partial representations in [2]}.
